HAL Id: cea-01908263
https://hal-cea.archives-ouvertes.fr/cea-01908263
Submitted on 30 Oct 2018
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of
sci-entific research documents, whether they are
pub-lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
Symbiotic equilibrium between Sodium Fast Reactors
and Pressurized Water Reactors supplied with MOX fuel
Guillaume Martin, C. Coquelet-Pascal
To cite this version:
Guillaume Martin, C. Coquelet-Pascal. Symbiotic equilibrium between Sodium Fast Reactors and
Pressurized Water Reactors supplied with MOX fuel. Annals of Nuclear Energy, Elsevier Masson,
2017, 103, pp.356 - 362. �10.1016/j.anucene.2017.01.041�. �cea-01908263�
Symbiotic equilibrium between Sodium Fast Reactors and Pressurized
Water Reactors supplied with MOX fuel
G. Martin
a,⇑, C. Coquelet-Pascal
ba
CEA – DEN/DER/SPRC/LECy, Bât. 230, 13108 Saint-Paul-Lez-Durance Cedex, France
b
CEA – DEN/DER/SPRC/LEDC, Bât. 230, 13108 Saint-Paul-Lez-Durance Cedex, France
a r t i c l e i n f o
Article history:
Received 14 September 2016
Received in revised form 25 January 2017 Accepted 28 January 2017 Keywords: Nuclear energy Plutonium Fast reactors SFR Thermal reactors Fuel reprocessing Symbiotic nuclear systems EPRTM
a b s t r a c t
The symbiotic equilibrium between 1.51 GWe breeder SFR (Sodium Fast Reactors) and 1.6 GWe EPRTM
(European Pressurized water Reactors) is studied. EPRTMare only supplied with MOX (Mixed OXide) fuel
to avoid the use of natural uranium. The equilibrium is studied by considering the flows of plutonium. Its isotopic composition is here described by a single real number referred to as the Pu grade. Plutonium flows through both reactor types are characterized by using linear functions of the Pu grade in new fuels. These functions have been determined by fitting data from a former scenario study carried out with the COSI6 simulation software.
Two different reprocessing strategies are considered. With joint reprocessing of all spent fuels, total and fissile plutonium flows balance for a unique fraction x of EPRTMin the fleet, equal to 0.2547. This x
value is consistent with the results reported in the former scenario study mentioned above. When EPRTMspent fuels are used in priority to supply SFR (distinct reprocessing), x reaches 0.2582 at most.
COSI6 simulations have been performed to further assess these results. The EPRTMfraction in the fleet
at symbiotic equilibrium barely depends on the applied reprocessing strategy, so that the more flexible joint reprocessing constitutes the reference option in that case.
Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction
Closing the fuel cycle is a major challenge to improve the sus-tainability of civil nuclear power, and complex systems have been
studied in this respect (see e.g.Gao and Ko, 2014; Lindley et al.,
2014). In this context, a symbiotic nuclear system denotes a fleet
composed of various reactor types: reactors which produce fissile
elements compensate for their consumption (Chersola et al.,
2015). Here, the main fissile element is plutonium, produced in
breeder SFR (Sodium Fast Reactors) and consumed in EPRTM
(Euro-pean Pressurized water Reactors) only supplied with MOX (Mixed OXide (U,Pu)O2) fuel. Indeed, a fleet composed of SFR and EPRTMcan
dispense with natural resources as long as some depleted or repro-cessed uranium is available to supplement Pu in new fuels.
A recent article (Martin et al., 2016) reported scenarios of the
French fleet evolving towards a nuclear system including both these reactor types exclusively. The mixed fleet at the end of the scenarios was composed of circa a quarter of EPRTM, so that the total
plutonium inventory was nearly steady, which indicates a fleet composition close to a symbiotic equilibrium when all irradiated fuels are reprocessed. Joint reprocessing of all spent fuels was
applied to improve the fuel management flexibility. Another viable strategy would have consisted in recycling the Pu from SFR spent fuels in EPRTM
in priority (distinct reprocessing). These two repro-cessing strategies are presented inFig. 1.
The aim of the present study is to assess the conditions under which a symbiotic equilibrium exists for each reprocessing strat-egy. The basic equations which drive the symbiotic equilibrium for a joint reprocessing of spent fuels are set up. They are solved by considering only the flows of plutonium, whose isotopic compo-sition is described by a single number referring to its grade. The way plutonium evolves under irradiation has been deduced from data collected from the previous scenario study mentioned above (Martin et al., 2016). The joint reprocessing strategy leads to a unique fleet composition at symbiotic equilibrium.
The symbiotic equilibrium between EPRTMand SFR applying
dis-tinct reprocessing of spent fuels is then described. Several
symbi-otic equilibriums are found. The fraction of EPRTM in the fleet is
maximal when all the plutonium introduced in EPRTM MOX fuels
comes from SFR spent fuels. Nevertheless the gain with respect to joint reprocessing appears marginal, which means that fissile plutonium savings associated to this complex reprocessing strat-egy remain quite low. In this context, joint reprocessing no doubt constitutes the reference option for such a symbiotic nuclear system.
http://dx.doi.org/10.1016/j.anucene.2017.01.041 0306-4549/Ó 2017 Elsevier Ltd. All rights reserved.
⇑Corresponding author.
E-mail address:guillaume.martin@cea.fr(G. Martin).
Contents lists available atScienceDirect
Annals of Nuclear Energy
2. Previous work
Mixed nuclear fleets composed of EPRTMand SFR were
previ-ously simulated (Martin et al., 2016) using the COSI6 scenario
soft-ware (Coquelet-Pascal et al., 2015), developed by CEA. COSI6 can
simulate in detail the time evolution of a nuclear reactor fleet with its associated fuel cycle facilities. New fuel compositions can be estimated by applying equivalence models. COSI6 was here
cou-pled with the CESAR5.3 code (Vidal et al., 2012) to calculate the
composition evolution of matters in pile or in storage conditions. CESAR5.3 solves the Bateman equation for 109 heavy nuclides and more than 200 fission products using JEFF3.1.1 nuclear data and one-group cross-section libraries for reactor modeling.
Two simulations of the French fleet evolving step by step (Chabert et al., 2015) towards a symbiotic nuclear system were run (Martin et al., 2016). They were built within the limits of con-servative criteria defined in concert with French industrialists (AREVA and EDF), so that they are realistic as regards our current
knowledge and feedback (Martin et al., 2016). Electricity
produc-tion curves of both scenarios are shown inFig. 2.
In these scenarios, EPRTMand SFR operate in diverse conditions
over several decades. In this respect all fuel batches passing
through breeder SFR (1076 batches) and EPRTM only fueled with
MOX (321 batches) during the progressive scenario (seeFig. 2.a)
provide a consistent reference dataset for describing the fuel
evo-lution in pile (see Section 3.2). The cores of these reactors are
respectively managed by thirds and fifths. Main characteristics of
simulated EPRTMand SFR are reported inTable 1.
At the end of the simulations, mixed nuclear fleets were
com-posed of 10 EPRTMwith 28 or 30 SFR. If the real number x stands
for the fraction of EPRTMin the fleet, simulations were carried out
at x¼ 0:2632 and x ¼ 0:25. These fleet compositions led to rather
stable plutonium inventories, but even so not strictly constant as
shown inFig. 3. A slight increase of the plutonium stock counts
for too much breeder SFR in the fleet (x¼ 0:25), whereas a
decrease counts for the opposite (x¼ 0:2632). Therefore one may
expect that the EPRTMfraction in the fleet which perfectly satisfies
the symbiotic equilibrium is comprised between these two values.
Fig. 1. Joint reprocessing (a) and distinct reprocessing (b) of EPRTM
and SFR spent fuels.
Fig. 2. Electricity production of EPRTM
and SFR during the progressive (a) and fast (b) transition scenarios to a symbiotic nuclear fleet (Martin et al., 2016). Table 1
Description of 1.51 GWe breeder SFR and of EPRTM
fueled with MOX only. Reactors EPRTM 100% MOX Breeder SFR CFV V1 Power (GWe) 1.60 1.51 Net yield (%) 35.6 40.3 Core mass (tHM) 125 129
Core composition MOX only 40% fissile 60% fertile Fuel need (tHM/yr) MOX: 25.4 fissile: 8.1 fertile: 8.7 Fissile fuel BU 53.5 GWd/t 116.3 GWd/t
Fig. 3. Evolution over 40 years of the total plutonium inventory associated to two mixed EPRTM
– SFR fleets (Martin et al., 2016), x being the EPRTM
3. Joint reprocessing 3.1. Description
Joint reprocessing of all spent fuels has first been considered. As
in similar scenario studies (Martin and Girieud, 2016), a minimal
cooling time of 5 years occurs between spent fuel unloading and reprocessing operations. Reprocessing essentially consists in extracting from spent fuels the plutonium which enters into
MOX fuel fabrication (for EPRTMand SFR). Then, at least two
addi-tional years elapse before a new MOX fuel can be loaded in reactor. The minimal time during which the plutonium decays before its recycling in pile is therefore of 7 years. The fuel cycle with joint reprocessing is illustrated inFig. 4.
InFig. 4are reported the parameters which describe the pluto-nium flows in the closed fuel cycle. NEand NSrepresent the Pu
con-sumptions of EPRTM
and SFR respectively, whereas PE and PSstand
for Pu productions. Joint reprocessing results in the same pluto-nium isotopic vector in all new fuels: G denotes its grade at symbi-otic equilibrium. In a general case, one can note that Pu grades should be defined as isotopic vectors whose size is the number of Pu isotopes present in irradiated fuels. Here however, the Pu grade has been reduced to a single real number according to the weight ratio(2)(see Section3.2). This way to proceed is further discussed in Section5.Table 2reports all parameters used along this article, some of them referring to the distinct fuel reprocessing strategy described in Section4.
All the isotopes present in the fuels in pile contribute to neutron capture and/or thermalization processes, and participate in the core neutron behavior. Here however, only plutonium isotopes are assumed in first order to impact the fuel flows drawn in
Fig. 4. It is then possible to write the conditions of the symbiotic
equilibrium with joint reprocessing as a system of two equations (see system(1)). x NEðGÞ þ ð1 xÞ NSðGÞ ¼ x PEðGÞ þ ð1 xÞ PSðGÞ G¼ð1 xÞ PSðGÞ
C
SðGÞ þ x PEðGÞC
EðGÞ ð1 xÞ PSðGÞ þ x PEðGÞ 8 < : ð1ÞThe first equation is here a balance between plutonium produc-tion and consumpproduc-tion. Pu need and producproduc-tion funcproduc-tions depend here upon the plutonium grade G. Only two Pu isotopes contribute
significantly to fissions inside the reactor core, namely239Pu and
241Pu. The second equation in system(1)provides that, with joint
reprocessing, the plutonium grade G in new fuels is a weighted average of plutonium grades in irradiated fuels unloaded from both reactor types (CE andCSfor EPRTMand SFR respectively). The
bal-ance of fissile Pu isotopes can be deduced by multiplying both
equations in system(2).
3.2. Assumptions
The plutonium grade is here described by a single real number.
The Pu grade does not include241Am (Martin et al., 2016) which
derives from241Pu and acts as a neutron absorber. This element
is usually accounted for since its concentration increases as Pu ages. However, in the steady-state fleet, the time interval between spent fuel unloading and the reloading in pile of the Pu that it con-tains should ideally not vary: the fastest possible recycling (7 years) applies since it constitutes the best option in terms of plu-tonium management. Steady Pu aging explains why the Pu grade
can be defined without241Am, according to relation(2).
g¼239PPuM¼244þ241Pu M¼236MPu
ð2Þ
Plutonium need, production and output grade functions here
characterize each reactor present in the mixed fleet: EPRTM and
SFR. These three functions for both reactor types depend on the
plutonium grade in new fuels. They are presented in Fig. 5 (6
graphs). Fuel batches from the progressive transition scenario
pre-viously simulated (Martin et al., 2016) (see Section2) have been
used to calculate them: these data appear as dots inFig. 5.
All the reactor functions have here been defined as linear func-tions of the plutonium grade in new fuels (seeFig. 5). This has been
partly inferred from the equivalence model for SFR (Baker and
Ross, 1963) which linearly depends on each Pu isotope concentra-tion, although this particular aspect of the simulations may be
improved (Krivtchik, 2014). For the period between spent fuel
unloading and the reloading of the Pu that it contains, only the decay of fissile241Pu, of half-life of 14.4 years, should significantly
impact the symbiotic equilibrium. A 7-year decay of 241Pu has
therefore been applied to fuel batches which were just irradiated to account for intermediate cooling, reprocessing and fuel fabrica-tion steps: this decay is accounted for inFig. 5.b, c, e and f. Pu losses during spent fuel reprocessing are neglected.
The fuels after irradiation in SFR show a large variety of pluto-nium contents and grades. Whereas high-grade Pu has been kept
for EPRTM MOX fuel fabrication since its Pu content should not
exceed a limit for safety reasons (Martin et al., 2016), the SFR
CFV core has a particularly large fuel acceptance (Buiron and
Dujcikova, 2015). Spent fuels containing low-grade plutonium, namely enriched reprocessed uranium, PWR MOX and mostly aged fuels, therefore supplied SFR as far as possible (Martin et al., 2016). As a consequence of this, plutonium isotopic composition in new SFR fuels varied strongly, which explains the dispersion of the
cor-responding outcomes (Fig. 5.e and f). In particular, fuel batches
with plutonium of similar grade g but different aging led to mark-edly different results.
Fig. 4. Fuel cycle of a mixed EPRTM
– SFR fleet with joint reprocessing of spent fuels.
Table 2 Symbol table.
Parameters Unit Description x 2 0; 1½ EPRTM
fraction in the fleet NE tHM/yr Pu consumption in an EPRTMreactor
NS tHM/yr Pu consumption in a SFR reactor
PE tHM/yr Pu output from an EPRTMreactor
PS tHM/yr Pu output from a SFR reactor
CE 2 0; 1½ Pu grade in EPRTMspent fuel
CS 2 0; 1½ Pu grade in SFR spent fuel
g 2 0; 1½ Plutonium grade in new fuel G; G
E; GS 2 0; 1½ Equilibrium Pu grades
E 2 0; 1½ EPRTMPu fraction recycled into EPRTM
3.3. Solution
The system of Eqs.(1)is solved in this section. The 2 unknowns
are the fleet composition (EPRTMfraction x) and the Pu grade in
fresh MOX fuels G at symbiotic equilibrium. The first equation in this system stands for the balance between total plutonium pro-duction and consumption. It leads to a collection of fleet
composi-tions (x values) as a function of the plutonium grade G at
equilibrium, as shown inFig. 6.
The second equation in system(1)can also be reduced to a
rela-tion between x and G. The system is therefore solved by
intersect-ing two functions xðGÞ, inferred from both equations in system(1)
(seeFig. 7). The mixed nuclear system of EPRTMand SFR with joint
reprocessing is symbiotic for a unique fleet composition,
corre-Fig. 5. Linear fits of the data relative to plutonium consumption, production and grade evolution (Martin et al., 2016) for both reactor types.
Fig. 6. Balance between Pu production (blue lines) and consumption (red lines) applying joint reprocessing of spent fuels. (For interpretation of the references to
sponding here to a fraction of EPRTMof 0.2547. As expected, this
fraction is included between 0.25 and 0.2632 (see Section2).
4. Distinct reprocessing 4.1. Description
Mean production on consumption ratios in breeder SFR have been calculated for total and fissile plutonium: lines reported in
Fig. 8 have been deduced from the linear regression functions
shown inFig. 5. The dots are derived from the results of the
previ-ous COSI6 simulation (Martin et al., 2016) (progressive transition
scenario). The considered breeder SFR core concept is usually
sup-posed to have a breeding ratio around 1.2 (Tiphine et al., 2015),
which actually corresponds here to the minimum of the average profit in fissile Pu after irradiation.
The green curve inFig. 8has been tabulated from the regression
lines inFig. 5.d, e and f (applying PSCS= NSg). It reveals that the
fis-sile Pu production in SFR is higher on average when the plutonium grade in fresh fuels decreases below 60%. Since plutonium grade from unloaded EPRTMfuels is inferior to 55% after 7 years of cooling,
as shown inFig. 5.c, a way to increase the fissile Pu production in
the mixed nuclear system would therefore consist in loading the
low grade Pu from EPRTM spent fuels in SFR in priority. Distinct
reprocessing of EPRTMand SFR spent fuels would be applied as
illus-trated inFig. 9.
Distinct reprocessing implies that the plutonium grades inside
new EPRTMand SFR MOX fuels are different. They are respectively
noted GE and GS. Whereas most of EPRTM spent fuels supply SFR,
plutonium whose grade has improved in SFR is mainly used to fab-ricate PWR MOX fuels. A fraction of the plutonium coming from SFR spent fuels may however be recycled into SFR at symbiotic
equilibrium, in case there is not enough Pu in EPRTM spent fuels
to feed them. In the same way a fraction of the Pu from EPRTMspent
fuels might be recycled into EPRTM
. Let
SandE be the spent fuelfractions self-recycled into SFR and EPRTMrespectively. A system
of four independent equations (see system(3)) can then be written
to describe the symbiotic equilibrium in case of distinct reprocess-ing of spent fuels.
x NEðGEÞ ¼ ð1 xÞ ð1
SÞ PSðGSÞ þ xEPEðGEÞ ð1 xÞ NSðGSÞ ¼ x ð1 EÞ PEðGEÞ þ ð1 xÞSPSðGSÞ GE¼ ð1 xÞð1 SÞ PSðGSÞC
SðGSÞ þ xEPEðGEÞC
EðGEÞ ð1 xÞð1 SÞ PSðGSÞ þ xEPEðGEÞ GS¼ ð1 xÞSPSðGSÞC
SðGSÞ þ xð1 EÞ PEðGEÞC
EðGEÞ ð1 xÞSPSðGSÞ þ xð1 EÞ PEðGEÞ ð3ÞThe two first equations stand for total plutonium balances at equilibrium. By summing their left and right members, it comes the first equation in system(1), i.e. the equilibrium between pluto-nium flows just before reactor loading. The two last equations in system(3)are relative to plutonium grades, i.e. to the flows of fis-sile plutonium isotopes.
4.2. Solution
Under the same set of assumptions applied above (see
Sec-tion3.2), the non-linear system(3)returns to a minimization
prob-lem that has been solved numerically using a GRG algorithm (Lasdon and Waren, 1983). Convergence is reached when the
v
2indicator calculated according to the relation(4)goes down below
109, with Li and Ri being the left and right members of the ith
equation in system(3).
v
2¼X i¼4 i¼1 Li Ri Li 2 ð4ÞThere are 5 degrees of freedom in system(3): x; G S; G
E;
SandE.Since it includes only 4 equations, this system has been solved by
setting one parameter. With
E¼ 0, a single set of values has beenfound at symbiotic equilibrium. Then increasing values of
Ehavebeen considered to solve the system and several EPRTMfractions x
at symbiotic equilibrium have been determined. They are reported inFig. 10.
The highest EPRTMfraction x is 0.2582, found when no plutonium
from EPRTMis recycled into EPRTM(
E¼ 0). As
Erises, x decreases.When
E is near 33.6%, the system converges to a solution forwhich
EþS¼ 1. This condition implies that the two lastequa-tions in system(3) are equivalent: it comes GE¼ GS¼ G, which
returns to joint reprocessing of spent fuels. The solution found in
Section3.3is confirmed (x¼ 0:2547). InTable 3are detailed the
solutions corresponding to x¼ 0:2582 (highest x value applying
distinct reprocessing) and x¼ 0:2547 (joint reprocessing).
The fractions of EPRTMin the fleet are barely distinct for both
reprocessing strategies. This is all the more true since in practice, this difference should be generally less than one power plant in a real nuclear fleet comprising a whole number of reactors. In this regard, the mixed fleet of 38 reactors at the end of the transition scenarios of the French fleet which was previously published (Martin et al., 2016) can be considered symbiotic, with
x¼ 0:2632 0:2547.
Fig. 8. Mean production on consumption ratios in a breeder SFR for total and fissile plutonium. The dots are derived from a previous study (Martin et al., 2016).
The slight increase of x when distinct reprocessing applies can-not be attributed to a higher fissile Pu production in SFR as expected initially. Indeed, the mean plutonium grade in SFR new fuels GSis 62.43%, implying lower total and fissile Pu productions
with regard to joint reprocessing (G¼ 63:36%) according to
Fig. 8. The production of fissile Pu isotopes in SFR would only be improved for Pu grades lower than 60 %, which would require more EPRTMin the fleet.
To explain this x difference, one has to consider the fissile Pu
consumption in EPRTM. The net consumption of fissile plutonium
isotopes in an EPRTM can be estimated by g N
EðgÞ PEðgÞCEðgÞ. It
decreases from 0.654 tHM/yr to 0.637 tHM/yr when GErises from
63:36% (joint reprocessing) to 65:84% (distinct reprocessing). This
effect is nonetheless an extrapolation since 65.84% lies outside the range of values covered by the EPRTMdataset (see dots inFig. 5.a, b
and c). This is why the solutions presented inTable 3have further
been assessed through additional COSI6 simulations.
5. COSI6 simulation
The symbiotic equilibriums reported inTable 3have been
sim-ulated using COSI6 (Coquelet-Pascal et al., 2015). In addition,
mixed fleets of same composition as those previously studied
(see Section2) have been simulated. Reprocessing has been
mod-eled as in the most recent scenarios built in collaboration with
the French industry (Chabert et al., 2015; Tiphine et al., 2015;
Martin et al., 2016). Besides, since it appeared impossible to model in practice precise reactor fractions using whole numbers of reac-tors, power plants have been modeled as parts of a single reactor unit. This amounts to considering, for instance, that the fuel stream
through x EPRTM
equal x times that of a reactor of 1.6 GWe. Ten
reactors have been operated in total (10 x EPRTM and
10 ð1 xÞ SFR). All the fractional reactors start within a same
5-year period. A Pu stock of around 500 tHM initially supplies MOX fuel fabrication plants when no spent fuel is still available. Poor and reprocessed uranium stocks are also withdrawn to make fertile and fissile fuels respectively. The simulations cover 500 years to ensure that a steady-state is reached. The total Pu inventories over the last 100 years of simulation are reported in
Fig. 11.
A fairly stable plutonium inventory is obtained from the x val-ues representative of joint reprocessing (0.2547) and distinct reprocessing of spent fuels (0.2582). However one can observe that the plutonium stock grows slowly. The low deviation from symbi-otic equilibrium can be attributed to the slight difference between the applied linear regressions and the highest values of plutonium
production (seeFig. 5). Indeed, the highest values of plutonium
production mostly correspond to a minimum aging of plutonium close to 7 years, used to equate the symbiotic equilibrium with plutonium isotopic vectors collapsed into single scalar vectors
(see Section3.2). Nevertheless, linear regressions are not far from
the highest values of Pu production and output grade data,
espe-cially for plutonium grades greater than 60% in SFR (see Fig. 5.e
and f). This explains why the deviation from a perfect Pu balance remains marginal.
These COSI6 simulations eventually assess the results obtained relatively to symbiotic equilibriums and further support that there is no significant difference in equilibrium fleet compositions for both reprocessing strategies. Therefore the more flexible joint reprocessing certainly constitutes a preferable option for the
stud-ied symbiotic nuclear system, composed of EPRTMand SFR.
6. Conclusion
The symbiotic equilibrium of a mixed fleet of 1.6 GWe EPRTMand
1.51 GWe breeder SFR is studied. EPRTMare fueled with MOX only: a
symbiotic equilibrium indeed consists in a balance between the consumption and the production of fissile elements without any supply of natural resources when all irradiated fuels are repro-cessed. The problem is tackled considering few simplifying assumptions:
Only plutonium is assumed to impact the symbiotic equilibrium.
A single real number, referred to as the Pu grade (see Eq.(2)), is supposed to account for the plutonium isotopic composition.
Fig. 10. Symbiotic equilibrium as a function of the spent fuel fractionE
self-recycled into EPRTM
.
Table 3
Solutions corresponding to the highest x value with distinct reprocessing and to joint reprocessing of spent fuels.
Variable Main results
Distinct reprocessing Joint reprocessing
x 0.2582 0.2547
GE 65.84% G¼ 63:36%
GS 62.43%
E 0 0.336
S 0.605 ð1 EÞ ¼ 0:664
Fig. 11. Evolution for 100 years of plutonium inventories during COSI6 simulation of mixed EPRTM
At least 7 years elapse between a spent fuel unloading operation and the in pile reintroduction of the Pu that it contains. A 7-year
decay of 241Pu is applied as regards this minimal Pu aging,
which optimizes plutonium management at equilibrium. The plutonium need, production and grade evolution which
characterize both irradiation sequences in EPRTM and SFR are
reduced to linear functions upon the Pu grade in new fuels. These functions have been determined from the results of a pre-vious scenario study (Martin et al., 2016) carried out with COSI6 (Coquelet-Pascal et al., 2015).
Two different reprocessing strategies are considered. With joint
reprocessing of all spent fuels, only a single EPRTM
fraction
x¼ 0:2547 in the fleet can balance total and fissile plutonium flows
(symbiotic equilibrium). As expected from a former study (Martin
et al., 2016), this x value lies well between 0.25 and 0.2632. When
the plutonium from EPRTMspent fuels supplies SFR in priority
(dis-tinct reprocessing), x may slightly increase up to 0.2582. This increase is mainly due to a lower net plutonium consumption in
EPRTMas the Pu grade in new fuels gets better. SFR breeding
perfor-mance does not improve in that case.
Additional COSI6 simulations have been carried out to further assess the symbiotic equilibriums which have been found. One
can therefore conclude that the EPRTMfractions in the fleet barely
stand apart at symbiotic equilibrium whatever the reprocessing strategy, since they should correspond to the same fleet composi-tion in practice (applying whole numbers of reactors). In this respect the more flexible joint reprocessing of spent fuels no doubt constitutes the reference option for the studied nuclear system.
Acknowledgments
The authors are grateful to AREVA and EDF for their support to this work through the ACF research program. In addition, they
thank the members of the working group on ‘‘ Industrial Scenarios” to have inspired this study.
References
Baker, A.R., Ross, R.W., 1963. Comparison of the value of plutonium and uranium isotopes in fast reactors. In: Proceedings of the conference on breeding, economics and safety in large fast reactors. Paper ANL 6792.
Buiron, L., Dujcikova, L., 2015. Low void effect (CFV) core concept flexibility: from self-breeder to burner core. In: Proceedings of ICAPP Paper 15091.
Chabert, C., Tiphine, M., Krivtchik, G., Allou, A., Saturnin, A., Girotto, J., Sarrat, P., Hancok, H., Mathonnière, G., Gabriel, S., Baschwitz, A., Fillastre, E., Giffard, F., Jasserand, F., Boullis, B., Leudet, A., Caron-Charles, M., Senentz, G., Carlier, B., Durpel, L.V.D., R.Grosman, Werf, J.V.D., Laugier, F., Settimo, D., Garzenne, C., 2015. Considerations on industrial feasibility of scenarios with the progressive deployment of Pu multi recycling in SFRs in the French nuclear power fleet. In: Proceedings of Global Paper 5351.
Chersola, D., Lomonaco, G., Marotta, R., 2015. The VHTR and GFR and their use in innovative symbiotic fuel cycles. Prog. Nucl. Energy 83, 443–449.
Coquelet-Pascal, C., Tiphine, M., Krivtchik, G., Freynet, D., Cany, C., Eschbach, R., Chabert, C., 2015. COSI6: a tool for nuclear transition scenarios studies and application to SFR deployment scenarios with minor actinides transmutation. Nucl. Tech. 192, 91–110.
Gao, F., Ko, W.I., 2014. Modeling and system analysis of fuel cycles for nuclear power sustainability (I): uranium consumption and waste generation. Ann. Nucl. Energy 65, 10–23.
Krivtchik, G., 2014. Analysis of Uncertainty Propagation in Nuclear Fuel Cycle Scenarios (Ph. D. thesis). Université de Grenoble.
Lasdon, L.S., Waren, A.D., 1983. Large scale nonlinear programming. Comput. Chem. Eng. 7, 159.
Lindley, B.A., Franceschini, F., Parks, G.T., 2014. The closed thorium-transuranic fuel cycle in reduced-moderation PWRs and BWRs. Ann. Nucl. Energy 63, 241–254. Martin, G., Girieud, R., 2016. Middle-term thorium strategy for PWR fleets. Energy
Policy 99, 147–153.
Martin, G., Tiphine, M., Coquelet-Pascal, C., 2016. French transition scenarios toward a symbiotic nuclear fleet. In: Proceedings of ICAPP Paper 15732. Tiphine, M., Coquelet-Pascal, C., Krivtchik, G., Eschbach, R., Chabert, C., Carlier, B.,
Caron-Charles, M., Senentz, G., Durpel, L.V.D., Garzenne, C., Laugier, F., 2015. Simulations of progressive potential scenarios of Pu multirecycling in SFR and associated phase-out in the French nuclear power fleet. In: Proceedings of Global Paper 5326.
Vidal, J.M., Eschbach, R., Launay, A., Binet, C., Thro, J.F., 2012. CESAR5.3: An industrial tool for nuclear fuel and waste characterization with associated qualification. In: Proceedings of the WM2012 conference, Phoenix, USA.
